Question

a sample was done, collecting the data below. calculate the standard deviation, to one decimal place.

Explanation:

Step1: Calculate the mean

The data set is \(x = \{6,22,18,27,25\}\). The mean \(\bar{x}=\frac{6 + 22+18+27+25}{5}=\frac{98}{5}=19.6\)

Step2: Calculate the squared - differences

\((6 - 19.6)^2=(-13.6)^2 = 184.96\), \((22-19.6)^2=(2.4)^2 = 5.76\), \((18 - 19.6)^2=(-1.6)^2=2.56\), \((27-19.6)^2=(7.4)^2 = 54.76\), \((25-19.6)^2=(5.4)^2=29.16\)

Step3: Calculate the variance

The variance \(s^2=\frac{184.96 + 5.76+2.56+54.76+29.16}{5 - 1}=\frac{277.2}{4}=69.3\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{69.3}\approx8.3\)

Answer:

8.3